The purpose of this project is to conduct research in mathematical statistics, probability, and applied mathematics in order to develop new statistical methodology applicable to biomedical sciences. We continue research into methods for designing epidemiologic studies with maximum power for equivalence testing, and have developed efficient methods for matched-pair designs. We also derived formulas for determining power and sample size requirements for equivalence testing based on the rate ratio estimated from matched samples and are investigating methods for testing equivalence with censored survival data. We continue to investigate methods of assessing inter-rater agreement, and have derived improved, efficient methods for making inferences about the kappa coefficient. We are continuing to investigate optimal methods for estimating the attributable risk, or etiologic fraction, and for calculating confidence intervals which correct for the negative bias in most current methods. We also continue investigations into methods for examining birth cohort and calendar period trends in disease rates. A computer program to implement the exact non-parametric methods for examining birth cohort trends is being improved, and development continues on a computer program implementing parametric methods for examining birth cohort and calendar period patterns of risk in age-period-cohort models. We continue developing methods for examining mutational spectra in a defined DNA sequence, including tests for whether a certain pattern of mutations occurs more frequently than expected by chance in a specific gene.